Question

You are asked to prepare 1.3 L of a HCN/NaCNbuffer that has a pH of 9.87 and an osmotic pressure of 1.00 atm at 298 K.

What masses of HCN and NaCN should you use to prepare the buffer? (Assume complete dissociation of NaCN.)

Answer 1

You can use the information about osmotic pressure to first calculate the total concentration of HCN and NaCN, and then using the Henderson Hasselbalch equation, you can calculate the ratio of CN- to HCN, and then the masses of each.

Osmotic pressure = π = iMRT where i is van't Hoff factor, in this case i = 3 because NaCN gives Na+ and CN-, and HCN give H+ and CN-. So you have H+, Na+ and CN- and i = 3. Solve for M.
M = π/(i)(R)T) = 1./(3)(0.082)(298) = 0.013 M
0.033 mol/L x 1.3 L = 0.0169 moles

pH = pKa + log [NaCN]/[HCN]

=>9.87 = 9.21 +  log [NaCN]/[HCN]

=> log [NaCN]/[HCN] = 0.66

So now you know the molarity is 0.013 M and the ratio of NaCN to HCN is 0.16 : 1.

From there, and knowing you need 1.3 liters, and knowing molar mass of HCN and molar mass of NaCN, you should be able to calculate how to make the buffer.
look up pKa for HCN, substitute in the equation and solve for the ratio [NaCN]/[HCN].
Once you have that, and you know you need 0.0446 moles, you can solve for the moles NaCN and moles of HCN, and from that you can calculate the mass of each.